A manufacturer of TV sets produced $600$ units in the third year and $700$ units in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find the production in
(i) the first year- ( a )
(ii) the $10^{t h}$ year- ( b )
(iii) $7$ years - ( c )
Find ( c )-( a )-( b )

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Solution

Let 'a' be the first term and 'd' be the common difference of the A.P formed
$a_{3} = a + 2 d = 600................. (i)$
And $a_{7} = a + 6 d = 700...... (i i)$
Solving equation (i) and (ii)
$a = 550$ and $d = 5$
(i) Production in the first year is 550 TV sets.
(ii) Production in the 10th year = $a_{10} = a + 9 d$
$= 550 + 9 (25)$
$= 550 + 225$
$= 775$
(iii) Total production in 7 years =
$S_{7} = \frac{7}{2} [2 (550) + (7 - 1) 25]$
$= 4375$ .
Thus, the total production in 7 years if of 7375 TV sets

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A manufacturer of TV sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find the production in (i) the first year- ( a ) (ii) the 10th year- ( b )(iii) 7 years - ( c ) Find ( c )-( a )-( b )